Texture paint on 2nd object is not working
before you do anything check your blend mode in 3d view by pressing n > Tool > brush setting > blend mode and set it to mix 



1) check if object is selected first

2) isolate object before painting by pressing num/ or ~ to toggle local view

3) make the clip start smaller. (3d view > press N for right panel to show up and view > clip start)


4) try saving your image before doing the actual painting then save blender file then go File > Revert and see if the issue still exist.
5) if all else fails just go to edit mode and press ctrl+shift+n to recalculate normals and try again painting it.